Oracle-Efficient Online Classification with Stochastic Inputs and Adversarial Outputs

Abstract:We consider contextual binary prediction with i.i.d. contexts from an unknown distribution and adaptively chosen losses. We show that a simple Follow-the-Perturbed-Leader algorithm with Gaussian perturbation for each observed context achieves the optimal $\widetilde O(\sqrt{T\log N})$ expected regret for a class of $N$ experts, while requiring one optimization-oracle call per round and no explicit enumeration of the class. For an infinite hypothesis class $\mathcal H$, the algorithm attains $\widetilde O(\sqrt{T\operatorname{VC}(\mathcal H)})$ regret. This resolves an open problem posed by Lazaric and Munos (2012), showing that hybrid classification is computationally as easy as statistical learning.

Machine Learning (cs.LG); Machine Learning (stat.ML)

arXiv:2609.33760 [cs.LG]

(or arXiv:2609.33760v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2609.33760 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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